Problem based on range of a real valued function:

Value of a function:

The value of a function y = ƒ(x) at x = a is shown by ƒ(a). It is calculated by putting x = a in ƒ(x)

Problem: If then calculate the range of f(x).

Key concept: If f(x) is in the form of P(x)/Q(x), where p(x) and Q(x) are polynomial function of second degree we take the concept of quadratic equation.x

Solution:             Consider  

Problem: Calculate the range of .

Key concept:     If in a function there is only single variable whose range if known, and may be easily search in terms of y, then we can use the range of that variable to Calculate the range of the provided function.

Solution:             

                              We know for any real x, x²≥0

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